A femtosecond laser generally indicates a pulse type laser in which an ultra-short laser pulse having a narrow pulse width of several femtoseconds (1 femtosecond=10 to 15 seconds) to several hundreds of femtoseconds in a time domain is repeatedly generated at a predetermined period. When such a femtosecond laser is observed in a frequency domain, it has a spectrum having a wide spectral width of several tens of nanometers. A large number of optical modes are distributed at regularly spaced frequency intervals in such a spectrum, and such a spectrum having a comb shape is called an optical comb.
A frequency of each of the optical modes constituting such an optical comb may be defined as a combination of two independent parameters, that is, a repetition rate (fr) determined by a length of a resonator and a carrier-envelope offset frequency (f0) determined by a difference between the group velocity and the phase velocity. That is, a frequency fi of an i-th optical mode is represented as follows.fi=ifr+f0 
The most general method for stabilizing the frequency of the optical comb is to lock two degrees of freedom (the repetition rate and the carrier-envelope offset frequency) of the optical comb. In stabilizing the repetition rate and the carrier-envelope offset frequency, generally, a physical length, an optical path length, or internal dispersion in the resonator is adjusted. Here, in the case of using the physical length, the optical path length, and dispersion adjusting elements (a piezoelectric actuator, a servomotor, a modulator, a pumping laser, a prism pair, and an element for adjusting the tilt of a mirror) in the resonator, both the repetition rate and the carrier-envelope offset frequency are changed.
As a method for stabilizing the frequency of the optical comb, a method for locking the repetition rate and the carrier-envelope offset frequency, which are the two independent parameters, to a rubidium or cesium atomic clock used as a frequency standard in a radio frequency domain on the basis of a phase-locked loop (PLL) method is widely used. In order to improve the stability in stabilizing the frequency of the optical comb, a method of using a separate external cw laser locked to an optical frequency standard such as an optical atomic clock, absorption lines of atoms and molecules, or a high-finesse cavity instead of a radio frequency standard has been developed, and is disclosed in U.S. Pat. Nos. 7,809,222 and 8,780,948.
In the related art disclosed in the above documents, a reference RF signal may be obtained by using a frequency divider in order to divide a repetition rate frequency in a predetermined integer ratio, and the frequency of the optical comb may be stabilized at a higher precision as compared with a case of using the radio frequency standard by stabilizing the carrier-envelope offset frequency obtained from an f-2f interferometer, and the beat signal between a cw laser and the nearest comb mode to the reference RF signal having a frequency, which is a specific integer ratio of the repetition rate.
However, in such a method, a separate external cw laser is required in order to stabilize the optical comb to the optical frequency standard or the high-finesse cavity. Therefore, a control circuit becomes complicated, and locking characteristics may become bad due to intrinsic noise generated in the external laser.